On some tests-based projection pursuit for elliptical symmetry of a high-dimensional distribution |
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Authors: | Ping Jing Lixing Zhu |
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Institution: | (1) Mathematics Lab, China University of Mining & Technology, 100083 Beijing, China;(2) Probability Lab, Institute of Applied Mathematics, Chinese Academy of Sciences, 100080 Beijing, China |
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Abstract: | Some test statistics of Kolmogorov type and Cramér-von Mises type based on projection pursuit technique are proposed for the
testing problem of sphericity of a high-dimensional distribution. The limiting distributions of the test statistics are derived
under the null hypothesis and under any fixed alternative. The asymptotic properties of bootstrap approximation are investigated.
Furthermore, for computational reasons, an approximation for the statistics, based on the number theoretic method, is suggested.
An erratum to this article is available at . |
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Keywords: | bootstrap approximation projection pursuit type statistic elliptical symmetry |
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